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FEDERAL RESERVE BANK OF SAN FRANCISCO
WORKING PAPER SERIES
Missing Growth from Creative Destruction
Philippe Aghion
College de France and London School of Economics
Antonin Bergeaud
London School of Economics
Timo Boppart
IIES, Stockholm University
Peter J. Klenow
Stanford University
Huiyu Li
Federal Reserve Bank of San Francisco
August 2018
Working Paper 2017-04
http://www.frbsf.org/economic-research/publications/working-papers/2017/04/
Suggested citation:
Aghion, Philippe, Antonin Bergeaud, Timo Boppart, Peter J. Klenow, Huiyu Li. 2018. “Missing
Growth from Creative Destruction,” Federal Reserve Bank of San Francisco Working Paper
2017-04. https://doi.org/10.24148/wp2017-04
The views in this paper are solely the responsibility of the authors and should not be interpreted as
reflecting the views of the Federal Reserve Bank of San Francisco or the Board of Governors of
the Federal Reserve System.Missing Growth from Creative Destruction
Philippe Aghion, Antonin Bergeaud
Timo Boppart, Peter J. Klenow, Huiyu Li∗
August 2018
Abstract
When products exit due to entry of better products from new
producers, statistical agencies typically impute inflation from surviving
products. This understates growth if creatively-destroyed products
improve more than surviving products. Accordingly, the market share of
surviving products should shrink. Using entering and exiting
establishments to proxy for creative destruction, we estimate missing
growth in U.S. Census data on non-farm businesses from 1983–2013. We
find: (i) missing growth is substantial — around half a percentage point
per year; but (ii) missing growth did not accelerate much after 2005, and
therefore does not explain the sharp slowdown in growth since then.
∗
Aghion: Collège de France and London School of Economics; Bergeaud: Banque de France;
Boppart: IIES, Stockholm University; Klenow: Stanford University; Li: Federal Reserve Bank of
San Francisco. We thank Raouf Boucekkine, Pablo Fajgelbaum, Gita Gopinath, Colin Hottman
and Stephen Redding for excellent discussions and Victoria De Quadros for superb research
assistance. Ufuk Akcigit, Robert Feenstra, Chang-Tai Hsieh, Xavier Jaravel, Chad Jones, Per
Krusell, Torsten Persson, Ben Pugsley, John Van Reenen, four referees, and numerous seminar
participants provided helpful comments. Any opinions and conclusions expressed herein are
those of the authors and do not necessarily represent the views of the Federal Reserve System
or the U.S. Census Bureau. All results have been reviewed to ensure that no confidential
information is disclosed.
12
1 Introduction
Whereas it is straightforward to compute inflation for an unchanging set of
goods and services, it is much harder to separate inflation from quality
improvements and variety expansion amidst a changing set of items. In the
U.S. Consumer Price Index (CPI), over 3% of items exit the market each month
(Bils and Klenow, 2004). In the Producer Price Index (PPI) the figure is over 2%
per month (Nakamura and Steinsson, 2008).
The Boskin Commission (Boskin et al., 1996) highlighted the challenges of
measuring quality improvements when incumbents upgrade their products. It
also maintained that the CPI does not fully capture the benefits of brand new
varieties. We argue that there exists a subtler, overlooked bias in the case of
creative destruction. When the producer of the outgoing item does not produce
the incoming item, the standard procedure at statistical offices is to resort to
some form of imputation. Imputation inserts the average price growth among
a set of surviving products that were not creatively destroyed.1 We think this
misses some growth because inflation is likely to be below-average for items
subject to creative destruction.2
Creative destruction is believed to be a key source of economic growth. See
Aghion and Howitt (1992), Akcigit and Kerr (2018), and Aghion, Akcigit and
Howitt (2014). We therefore attempt to quantify the extent of “missing
growth”—the difference between actual and measured productivity
growth—due to the use of imputation in cases of creative destruction. Our
estimates are for the U.S. nonfarm business sector over the past three decades.
1
U.S. General Accounting Office (1999) details CPI procedures for dealing with product
exit. For the PPI, “If no price from a participating company has been received in a particular
month, the change in the price of the associated item will, in general, be estimated by averaging
the price changes for the other items within the same cell for which price reports have
been received.” (U.S. Bureau of Labor Statistics, 2015, p.10) The BLS makes explicit quality
adjustments, such as using hedonics, predominantly for goods that undergo periodic model
changes by incumbent producers (Groshen et al., 2017).
2
A similar bias due to creative destruction could arise at times of regular rotation of items in
the CPI and PPI samples.3 In the first part of the paper we develop a growth model with (exogenous) innovation to provide explicit expressions for missing growth. In this model, innovation may either create new varieties or replace existing varieties with products of higher quality. The quality improvements can be performed by incumbents on their own products, or by competing incumbents and entrants (creative destruction). The model predicts missing growth due to creative destruction if the statistical office resorts to imputation. In the second part of the paper we estimate the magnitude of missing growth based on our model. We use micro data from the U.S. Census on employment at all private nonfarm businesses to estimate missing growth from 1983–2013. We look at employment shares of continuing (incumbent), entering, and exiting plants. If new plants produce new varieties and carry out creative destruction, then the inroads they make in incumbents’ market share should signal their contribution to growth. Our findings can be summarized as follows. First, missing growth from imputation is substantial: roughly one-half a percentage point per year, or around one-third of measured productivity growth. Second, we find only a modest acceleration of missing growth since 2005, an order of magnitude smaller than needed to explain the slowdown in measured growth. Example: The following numerical example illustrates how imputation can miss growth. Suppose that: (i) 80% of products in the economy experience no innovation in a given period and are subject to a 4% inflation rate; (ii) 10% of products experience quality improvement without creative destruction, with their quality-adjusted prices falling 6% (i.e., an inflation rate of -6%); and (iii) 10% of products experience quality improvement due to creative destruction, with their quality-adjusted prices also falling by 6%. The true inflation rate in this economy is then 2%. Suppose further that nominal output grows at 4%, so that true productivity growth is 2% after subtracting the 2% true inflation rate. What happens if the statistical office resorts to imputation in cases of
4
creative destruction? Then it will not correctly decompose growth in nominal
output into its inflation and real growth components. Imputation means that
the statistical office will ignore the goods subject to creative destruction when
computing the inflation rate for the whole economy, and only consider the
products that were not subject to innovation plus the products for which
innovation did not involve creative destruction. Thus the statistical office will
take the average inflation rate for the whole economy to be equal to
8 1
· 4% + · (−6%) = 2.9%.
9 9
Presuming it correctly evaluates the growth in nominal GDP to be 4%, the
statistical office will (incorrectly) infer that the growth rate of real output is
4% − 2.9% = 1.1%.
This in turn implies “missing growth” in productivity amounting to
2% − 1.1% = 0.9%.
This ends our example, which hopefully clarifies the main mechanism by which
imputation can miss growth from creative destruction.3
Our paper touches on the recent literature about secular stagnation and
growth measurement. Gordon (2012) argues that innovation has run into
diminishing returns, inexorably slowing TFP growth.4 Syverson (2016) and
Byrne, Fernald and Reinsdorf (2016) conclude that understatement of growth
in the ICT sector cannot account for the productivity slowdown since 2005. In
contrast to these studies, we look at missing growth for the whole economy,
not just from the ICT sector.
3
This example is stylized. In practice, imputation by the BLS is carried out within the items
category or category-region. See the U.S. General Accounting Office (1999).
4
Related studies include Jones (1995), Kortum (1997), and Bloom et al. (2017).5
More closely related to our analysis are Feenstra (1994), Bils and Klenow
(2001), Bils (2009), Broda and Weinstein (2010), Erickson and Pakes (2011),
Byrne, Oliner and Sichel (2015), and Redding and Weinstein (2016).5 We make
two contributions relative to these important papers. First, we compute
missing growth for the entire private nonfarm sector from 1983–2013.6 Second,
we focus on a neglected source of missing growth, namely imputation in the
event of creative destruction. The missing growth we identify is likely to be
exacerbated when there is error in measuring quality improvements by
incumbents on their own products.7
The rest of the paper is organized as follows. In Section 2 we lay out an
environment relating missing growth to creative destruction. In Section 3 we
estimate missing growth using U.S. Census data on plant market shares.
Section 4 compares our estimates to those in three existing studies. Section 5
concludes.
2 A model of missing growth
In this section we relate our measure of missing growth to Feenstra (1994). We
modify his approach to focus on bias from new producers of a given product
5
Feenstra (1994) corrects for biases in the U.S. import price indices of six manufacturing
goods, in particular due to an expanding set of available product varieties. Bils and Klenow
(2001) use the U.S. Consumer Expenditure surveys to estimate “quality Engel curves” and
assess the unmeasured quality growth of 66 durable goods which account for 12% of consumer
spending. Bils (2009) uses CPI micro data to decompose the observed price increases of durable
goods into quality changes and true inflation. Broda and Weinstein (2010) look at missing
growth from entry and exit of products in the nondurable retail sector, using an AC Nielsen
database. Byrne, Oliner and Sichel (2015) look at missing growth in the semiconductor sector.
6
Broda and Weinstein (2010) used AC Nielsen data from 1994 and 1999–2003. This database
is heavily weighted toward nondurables, particularly food. Bils and Klenow (2004) report a
product exit rate of about 2.4% per month for nondurables (1.2% a month for food) versus about
6.2% per month for durable goods. Hence, it is important to analyze missing growth across
many sectors of the economy, including durables.
7
Unlike Broda and Weinstein (2010), we do not assume that the BLS makes no effort
to quantify such quality improvements. Bils (2009) estimates that the BLS subtracted
0.7 percentage points per year from inflation for durables over 1988–2006 due to quality
improvements. For the whole CPI, Moulton and Moses (1997) calculate that the BLS subtracted
1.8 percentage points in 1995.6
line, as opposed to all new products. This allows us to highlight the role of
creative destruction in missing growth, as opposed to quality bias from
incumbent improvement of their own products.
2.1 Relating missing growth to market share dynamics
Time is discrete and in each period consumption has a CES structure
σ
Z Nt σ−1
σ−1
Ct = [qt (j) ct (j)] σ dj , (1)
0
where ct (j) denotes quantity and qt (j) the quality of variety j. Nt is the number
of varieties available, which can change over time. Here σ > 1 denotes the
constant elasticity of substitution between varieties.
Let πt denote true inflation, the log first difference between t − 1 and t in the
minimum cost of acquiring one unit of composite C. Following Feenstra (1994)
we can decompose true inflation as
1 SIt ,t−1
bt −
πt = π log , (2)
σ−1 SIt ,t
where π
bt is inflation for a subset of products denoted It , and SIt ,τ is the share
in nominal expenditure spent on this set of products at time τ . Here π
bt can be
Sj,τ
constructed from the nominal expenditure shares sIt ,τ (j) ≡ SIt ,τ
and quality-
adjusted prices of products pτ (j)/qτ (j) within the subset It as
Z
pt (j)/qt (j)
bt ≡
π f (j, {sIt ,t−1 (i), sIt ,t (i)}i∈It ) log dj, (3)
j∈It pt−1 (j)/qt−1 (j)
where f (j, {sIt ,t−1 (i), sIt ,t (i)}i∈It ) is the Sato-Vartia weight.8
8
Sato-Vartia weights are
sIt ,t (j)−sIt ,t−1 (j)
log sIt ,t (j)−log sIt ,t−1 (j)
f (j, {sIt ,t−1 (i), sIt ,t (i)}i∈It ) = R sIt ,t (i)−sIt ,t−1 (i)
.
i∈It log sIt ,t (i)−log sIt ,t−1 (i)
di7
Feenstra (1994) chose It to be the set of U.S. import category-country pairs
that overlapped between t − 1 and t. If the U.S. import price index is captured
by π
bt , then the second term in (2) reflects inflation bias due to the changing
set of category-country pairs. Intuitively, if the market share of the subset of
products used for measurement changes, then this subset is not representative.
In particular, if the market share of the subset It is shrinking, then the relative
price of the subset must be rising. For a given change in market shares, the bias
is smaller when the σ elasticity is higher, because a smaller relative price change
is needed to explain the observe change in market shares.
Broda and Weinstein (2010) chose It to be the set of UPC codes in AC
Nielsen scanner data with positive sales in adjacent periods. They argue that
quality is fixed over time for a product with a given UPC code. They therefore
infer bias in measured inflation à la Feenstra from the change in market share
of overlapping UPC codes. This assumes that all quality growth is missed in
inflation measurement, including improvements by incumbents on their own
products. In practice, statistical offices do attempt to measure quality changes
and net them out of inflation, in particular for incumbent product upgrades.9
Our focus is on whether imputation leads to missing growth — in particular
in cases of creative destruction. We therefore define the subset of products It as
those produced by the same producer in overlapping periods. This is broader
than the set used by Broda-Weinstein since it includes successive generations
of products in a given line produced by the same firm. The omitted set of
goods is exiting and entering producer-product pairs. As we argue in our
Online Appendix A, the BLS infers inflation for these entering and exit
producer-product pairs using the inflation rate for continuing pairs. If the
market share of overlapping pairs is shrinking over time, however, then the
inflation rate of continuing pairs overstates overall inflation and understates
real growth. Thus, when the market share of continuing pairs shrinks, we infer
missing growth from creative destruction and/or brand new varieties.
9
See Table 1 in Groshen et al. (2017) and Table B1 in Moulton (2018).8
We make these links explicit in the next subsection by adding a supply to
side to the model with growth coming from quality improvements by
incumbent producers on their own products, creative destruction, and new
variety creation. In the next section we describe how we implement this
modified Feenstra approach on U.S. Census establishment data.
2.2 Framework of creative destruction and missing growth
There is a representative household supplying inelastically L units of labor
each period
and maximizes (1) subject to a budget constraint
R Nt
Πt + Wt L = 0 pt (j)ct (j)dj, where Πt and Wt L denotes profits and labor
earnings.
On the supply side, each variety c(j) is produced one-for-one with labor
ct (j) = lt (j),
by a monopolistically competitive producer, where lt (j) is the amount of labor
used to produce good j in period t. Given the isoelastic demand that results
from the household problem, it is optimal for each producer to set the price
σ
pt (j) = Wt , (4)
σ−1
where Wt is the nominal wage that equalizes across firms in the competitive
labor market. We assume the nominal wage follows an exogenously given path
over time which will imply that the other nominal variables like prices, p(j),
profits, Π, and nominal output will grow at the same rate over time.
We model technical change as product innovation.10 At each point in time,
10
This modeling choice matters in our empirical context since pure process innovation is
arguably more likely to be captured by the statistical office. Yet, across firms and plants with
price information in the Census of Manufacturing, we find that firm/plant revenues increase
without a decline in unit prices. This suggests that innovations are rather of the product than
of the process type. Hottman, Redding and Weinstein (2016) provide similar evidence for retail
prices of consumer nondurable manufacturers.9
and for each variety j there is a common exogenous probability of creative
destruction λd ∈ [0, 1). I.e., with probability λd the incumbent firm of input j is
replaced by a new producer. We assume that the new producer (who may be
an entrant or an incumbent firm) improves upon the previous producer’s
quality by a factor γd > 1. The previous producer cannot profitably produce
due to limit pricing by the new producer.11 If j is an existing variety where
quality is improved upon by a new producer, we have
qt (j) = γd qt−1 (j).
We refer to this innovation process as creative destruction.
In addition, for products j where the incumbent producer is not eclipsed by
creative destruction, there is each period an exogenous arrival rate λi ∈ [0, 1) of
an innovation that improves their by factor γi > 1. Hence, if j is a variety where
quality is improved upon by the incumbent producer, we have
qt (j) = γi qt−1 (j).
We call this incumbent own innovation. The main difference from creative
destruction is that the producer of j changes with creative destruction,
whereas it stays the same with incumbent own innovation. The arrival rates
and step sizes of creative destruction and incumbent own innovation are
constant over time and across varieties.
Finally, each period t, a flow of λn Nt−1 new product varieties ι ∈ (Nt−1 , Nt ] are
created and available to final goods producers from t onward. Consequently,
the law of motion for the number of varieties is
Nt = (1 + λn )Nt−1 .
11 σ
We assume γd > σ−1 and Bertrand competition within each market, which allows the new
producer, who produces a better product at the same cost as the current producer, to drive the
current producer out of the market.10
We allow the (relative) quality of new product varieties to differ from the
“average” quality of pre-existing varieties by a factor γn .12
To summarize, there are three sources of growth in this framework: First, the
quality of some products increases due to creative destruction. Second, for some
other products quality increases as a result of incumbent own innovation. Third,
new product varieties are invented which affects aggregate output, because the
utility function (1) features love-for-variety.
True, measured and missing growth There are no investment goods so that
aggregate nominal output equals aggregate nominal consumption
13
expenditure. Nominal expenditure can be expressed as Pt Ct where
R 1/(1−σ)
Nt 1−σ
Pt ≡ 0 (pt (j)/qt (j)) dj is the quality-adjusted ideal price index. In
Ct
this economy the real (gross) output growth gt = Ct−1
is given by nominal
Pt
output growth divided by the inflation rate Pt−1
.
As we show in Online Appendix B, the true growth rate in the economy is
1
g = 1 + λd γdσ−1 − 1 + (1 − λd )λi γiσ−1 − 1 + λn γnσ−1 σ−1 .
(5)
This equation shows how the arrival rates and step sizes affect the growth rate.
The term λn γnσ−1 captures the effect of variety expansion on growth, and the
growth rate is increasing in λn and γn . The term (1 − λd )λi γiσ−1 − 1
summarizes the effect of incumbent own innovation on growth. The term
12
More formally, we assume that a firm that introduces in period t a new variety ι starts with
a quality that equals γn > 0 times the “average” quality of pre-existing varieties j ∈ [0, Nt−1 ] in
period t − 1, that is
1
! σ−1
Z Nt−1
1 σ−1
qt (ι) = γn qt−1 (j) dj , ∀ι ∈ (Nt−1 , Nt ].
Nt−1 0
Average quality here is the geometric average, which depends on the elasticity of substitution.
We do not put further restrictions on the value of γn so that new products may enter the market
with above-average (γn > 1), average (γn = 1) or below-average quality (γn < 1). As the relative
quality of new varieties is a free parameter, expressing it this way is without loss of generality.
13
In an Online Appendix C we allow for capital and show how this affects the interpretation
of our missing growth estimates relative to measured growth.11
λd γdσ−1 − 1 captures the effect from creative destruction on the growth rate.
Next we turn to measured growth. We posit that the statistical office resorts
to imputation in response to producer-product entry and exit (we argue this is
realistic in Online Appendix A). That is, they presume the set of continuing
producer-product pairs is representative of the economy-wide inflation rate.14
For the products that are not subject to creative destruction we assume that
statistical agency observes unit prices correctly. Their quality adjustments
allow them to retrieve the true frequency and step size of quality
improvements by incumbents on their own products. As we show in our
Online Appendix B, under these assumptions, the measured real growth rate is
then
1
gbt = 1 + λi γi σ−1 − 1 σ−1 .
(6)
We then define the log difference between true growth and measured growth
as missing growth (M G). Combining (5), and (6), allows us to approximated
missing growth as15
λd γdσ−1 − 1 + λn γnσ−1 − λd λi γiσ−1 − 1
M Gt ≈ . (7)
σ−1
The first two terms are growth from creative destruction and new varieties,
respectively. They are not missed entirely because growth is imputed based on
incumbent own innovations in the event of creative destruction, which
accounts for the last term. Growth is missed when the rate of innovation from
creative destruction and new varieties exceeds that imputed from continuing
producer-product pairs. Equation (7) allows us to theoretically decompose
missing growth into its sources — creative destruction and variety expansion.
14
BLS imputation is actually carried out within categories or category-regions. See the U.S.
General Accounting Office (1999).
15
The exact growth rate is
log 1 + λd γdσ−1 − 1 + (1 − λd )λi γiσ−1 − 1 + λn γnσ−1 − log 1 + λi γiσ−1 − 1
M Gt = .
σ−112
Under the appropriate definition of the subset of products It , missing growth
can again be expressed in terms of formula (2) above as
1 SIt ,t−1
b t − πt =
M Gt = π log , (8)
σ−1 SIt ,t
where measured inflation π
bt is as defined in equation (3). Importantly, as
discussed, we define the set of overlapping products It in (3) as the set of
continuing producer-product pairs. Growth is missed when the market share of
these continuing pairs shrinks over time.
In our Online Appendix D, we derive missing growth when the quality
improvement of incumbents is not perfectly measured. In particular, we show
that missing growth due to creative destruction would be larger if quality
improvements by incumbents are understated, precisely due to imputation.
3 Estimates of missing growth
Here we present estimates of missing growth using data on the market share of
entering establishments (plants), surviving plants, and exiting plants. This
approach does not allow us to differentiate between the different sources of
missing growth (creative destruction vs. variety expansion), but it provides a
simple and intuitive quantification which avoids having to estimate the size
and frequency of the various types of innovations.
3.1 Measuring the market share of continuers
Our goal is to quantify missing growth in the aggregate economy over a time
horizon of several decades. We therefore base our estimates of missing growth
on the Longitudinal Business Database (LBD), which covers all nonfarm
business sector plants with at least one employee. We use the employment
information in this dataset to infer the market share of continuing plants, SIt ,t .
Ideally we would have data at the product level for each firm. Unfortunately,13 such data does not exist for the aggregate U.S. economy outside of the Census of Manufacturing, or consumer nondurables in the AC Nielsen scanner data. In lieu of such ideal data, we suppose that firms must add plants in order to produce new products. Such new plants could be at entering firms or at existing firms. And the products produced by new plants could be brand new varieties or the result of creative destruction. Moreover, we assume that all incumbent own innovation occurs at existing plants. Under these assumptions, we can use continuing plants as a proxy for continuing incumbent products. These assumptions are admittedly strong. They require that firms do not add products through existing plants. Bernard, Redding and Schott (2011) find that U.S. manufacturing plants do start up production in new industries. Our assumption may be a better approximation outside manufacturing, such as in retail where location is a key form of product differentiation. Related, if creative destruction occurs through process innovations embodied in new establishments (e.g., new Walmart outlets), then the market share of new plants should in principle capture them. If existing plants do introduce new varieties or carry out creative destruction, then our approach is likely to understate missing growth. As we explain below, our baseline specification will assess market shares of new plants after a 5 year lag. Hence, the critical assumption is that plants do not add new products after the age of 5 years. We can offer two facts that provide some reassurance here. First, employment growth is much lower after age 5 than for younger plants (Haltiwanger, Jarmin and Miranda, 2013). Second, plant exit rates do fall with age, but not very sharply after age 5 (Garcia-Macia, Hsieh and Klenow, 2018). If plants add varieties after age 5, then one would expect exit rates to fall rapidly beyond age 5. Our baseline estimates use employment data to measure market shares, rather than revenue or even payroll data. In our model these variables are all proportional to each other across products. But in practice they differ. Annual revenue data are only available at the firm level. Plant level revenue data is
14
available to us only every 5 years in the manufacturing sector. As a robustness
check we will report results with revenue for manufacturing. And we will show
robustness to using payroll rather than employment for all sectors.
To be more exact, we calculate market shares using plant data as follows.
Let B denote the first year of operation and D denote the last year of operation
of a plant. Then the continuing plants It are those plants who operated in both
t − 1 and t, that is, all plants with B ≤ t − 1 and D ≥ t. Define Et as the group of
plants that first operated in period t (B = t, D ≥ t) and Xt as the group of
plants that last operated in period t (B ≤ t, D = t). Let L(t, M) denote the total
employment in period t of plants belonging to group M. We then measure the
SIt ,t−1
ratio SIt ,t
on the right-hand side of (2) as
L(t − 1, It )
SIt ,t−1 L(t − 1, It ) + L(t − 1, Xt−1 )
= , (9)
SIt ,t L(t, It )
L(t, It ) + L(t, Et )
According to (9), missing growth is positive whenever the employment share of
continuing plants shrinks between t − 1 and t.
We define a period t as a calendar year, and map D to the last year a plant is
in LBD. We set B equal to k ≥ 0 years after the plant first appears in the LBD. If τ
is the first year the plant appears in the database, we set B = τ + k. We use k = 5
in our baseline specification.
3.2 Elasticities of substitution
To quantify missing growth we need the elasticity of substitution across plants
in all nonfarm business sectors. Hall (2018) estimates markups for 18 2-digit
sectors using KLEMS data for 1988-2015.16 He regresses industry output growth
on share-weighted input growth instrumented by military purchases and oil
prices, in the hopes that these are orthogonal to residual productivity growth.
16
Hall estimates that markups are modestly (but not precisely) trending up over time. His
sample period is close to our 1983–2013 LBD sample time frame.15
We convert Hall (2018)’s estimated markups to elasticities assuming the
σ
markups equal σ−1
. We display the implied elasticities for each 2-digit sector in
the first few columns of Table 1. In a few of the industries, Hall (2018) reports
markups that are less than one. In these industries (health care, construction
and education), we assume σ → ∞. As shown in the Table, Hall (2018)’s
implied σ’s range from below 3 to over 26 in the industries with markups in
excess of one.
3.3 Results
Our baseline results calculate missing growth from 1983–2013 using LBD data.
The LBD contains data on employment and payroll going back to 1976, but the
payroll data features a number of implausible outliers before 1989. We
therefore use employment data for our baseline estimates. Using the
employment data, we identify entrants beginning in 1977. 1983 is the earliest
year we can calculate missing growth (market share growth of survivors
between 1982 and 1983) because we use plants that have been in the data for at
least 5 years (1977 to 1982 at the beginning). We examine missing growth
starting in 1983.17
In the fourth column of Table 1, we report our missing growth estimates for
each 2-digit sector using Hall (2018)’s implied σ’s. We order the sectors by their
contribution to missing growth on average over 1983–2013, which totals 54 basis
points per year.18 The biggest contributors, by far, are NAICS 72 (hotels and
17
More specifically, we calculate missing growth in each year t using data from years t − 6,
t − 5, t − 1 and t. We use data in year t − 6 to identify plants that have been in the data for at
least 5 years in t − 1 and calculate their total employment in year t − 1. Then we calculate the
share of this total employment belonging to plants that survive to year t. Similarly, we use year
t − 5 data to identify plants that are in the data for at least 5 years in t and calculate the t period
employment share of plants surviving from period t − 1.
18
We aggregate using Tornqvist averages of the current and previous year employment shares
of the sector; this is a second order approximation to any smooth utility aggregator of 2-digit
sectors. We calculate the contribution of a sector in a year by multiplying the missing growth in
that sector with the Tornqvist employment share. Then we take averages over 1983 to 2013 to
arrive at the average contribution reported in the table.16
Table 1: AVERAGE MISSING GROWTH 1983–2013 BY 2- DIGIT SECTORS
Hall σ Missing Contribution
NAICS Sector name growth (ppt) (ppt) (%)
72 Hotels & Restaurants 2.82 2.70 0.18 33.9
44-45 Retail Trade 3.22 1.23 0.15 28.6
54 Professional Services 4.23 1.07 0.05 8.6
52 Finance and Insurance 3.17 0.60 0.03 5.4
81 Other Services 4.03 0.54 0.02 4.4
48-49 Transportation & Warehousing 4.23 0.58 0.02 3.7
71 Arts, Entertainment 2.92 1.51 0.02 3.6
51 Information 3.56 0.88 0.02 3.4
42 Wholesale Trade 4.70 0.29 0.01 2.5
31-33 Manufacturing 3.44 0.05 0.01 2.2
56 Admin & Support Services 26.0 0.21 0.01 1.7
55 Management of Companies 6.26 0.13 0.01 0.9
53 Real Estate 12.1 0.24 0.00 0.6
22 Utilities 9.33 0.16 0.00 0.3
21 Mining 4.85 0.37 0.00 0.3
62 Health Care ∞ 0 0 0
23 Construction ∞ 0 0 0
61 Education ∞ 0 0 0
Total 0.5417
restaurants) and 44-45 (retail trade); they contribute 33 of the 54 basis points,
or over 62% of the total. Their contribution may reflect the geographic spread
of outlets by big national chains. No other sector contributes more than 5 basis
points and we find very little missing growth in manufacturing.
The variation in missing growth across sectors in Table 1 suggests that
official relative price trends across sectors may be biased considerably. Taken
at face value, our estimates alter the pattern of Baumol’s cost disease cross
sectors.
Table 2: M EASURED VS . T RUE G ROWTH WITH H ALL σ’ S
Missing Measured “True” % of growth
Growth Growth Growth missed
1983–2013 0.54 1.87 2.41 22.4%
1983–1995 0.52 1.80 2.32 22.4%
1996–2005 0.48 2.68 3.16 15.2%
2006–2013 0.65 0.98 1.63 39.9%
Notes: Entries are percentage points per year. Missing growth is
calculated using equation (2). The market share is measured as
the employment share of plants in the Census Longitudinal Business
Database (LBD) as in (9). These baseline results assume a lag k = 5
and use the 2-digit elasticities of substitution in Hall (2018). Measured
growth is calculated as the BLS MFP series + R&D contribution
expressed in labor-augmenting terms. True growth is the sum of
measured growth and missing growth.
Table 2 compares our missing growth estimates to official TFP growth. The
entries are annual percentage points. As mentioned, we find 0.54 percentage
points of missing growth per year from 1983–2013. BLS measured TFP growth
over the same interval was 1.87 percentage points per year.19 If we add our
19
We put BLS TFP growth in labor-augmenting form, and include the BLS estimates of the
contribution of R&D and intellectual property to TFP growth. The BLS multifactor productivity
series uses real output growth from the BEA. The vast majority of the price indices that go into
constructing BEA real output growth come from the BLS (see U.S. Bureau of Economic Analysis,
2014), even if the BEA weights sectors differently than in the aggregate CPI or PPI.18
missing growth to the BLS TFP series we arrive at “true” growth of 2.41% per
year. Thus our baseline estimate is that over one-fifth of true growth is missed.
Table 2 also breaks the 30 year sample into three sub-periods: 1983–1995
(an initial period of average official growth), 1996–2005 (a middle period of
rapid official growth), and 2006–2013 (a final period of low official TFP growth).
Did missing growth contribute to the speedup or slowdown? Our estimates say
yes, but modestly at most. Missing growth slowed down by 4 basis points when
official growth accelerated by 88 basis points in the middle period. And
missing growth sped up by 17 basis points when official growth dropped 170
basis points in the final period.
While missing growth did not accelerate significantly in the aggregate, it did
so in the Information sector. In this sector, missing growth rose from 0.22
percent per year over 1983–2013 to 0.90 over 1996–2005 and to 1.90 over
2006–2013. Due to its small employment share, however, the Information
sector contributed a small amount to overall missing growth: 0.00 over
1983–2013, 0.02 over 1996–2005 and 0.04 over 2006–2013.
3.4 Robustness and discussion
In this section we discuss how our estimates of missing growth are affected by
the elasticity of substitution, the lag used to defined new plants, and the data
used to measure market shares (e.g., using payroll instead of employment data).
Elasticities of substitution As a robustness check, we use the Visa data to
estimate σ for the two sectors responsible for 57% of the total missing growth
in Table 1: retail trade and restaurants.20 Following the methodology of Dolfen
et al. (2018), we estimate σ by using the location of Visa cardholders vs.
20
In Table 1, Retail Trade contributed 28.6% of the total missing growth whereas Hotels and
Restaurants contributed 33.9%. We calculate the contribution of Retail Trade plus Restaurants
by 28.6% + 33.9% × 83.8% = 57.0% where 83.8% is the share of Restaurant employment (NAICS
722) in Hotels and Restaurants employment (NAICS 72) in the 2012 Census of Accommodation
and Food Services.19
physical stores and converting distance into effective price variation, based on
the opportunity cost of time and the direct costs of travel. We add the
differential travel costs to the average spending per visit at the store. Using all
cards, we regress relative visits on relative prices across stores to estimate the
elasticity of substitution in a given sector:
cij qj pjk + τij
log = log − (σ − 1) log . (10)
cik qk pjk + τik
Here i denotes a cardholder, j and k are competing merchants, c refers to the
number of visits, q denotes residual quality (assumed to be orthogonal to
customer distance to merchant j versus k), pjk is the average card spending per
visit at merchants j and k, and the τ ’s are estimated costs of travel.21
We only compare stores of competing chains within 3-digit NAICS (e.g.,
general merchandisers Walmart vs. Target, or grocery stores Trader Joe’s vs.
Whole Foods). Across restaurants (NAICS 722) we estimate an elasticity of
substitution of 2.92, not far from Hall (2018)’s estimate of 2.82. Across retail
establishments (NAICS 44-45), we estimate an elasticity of 5.01, higher than
Hall’s estimate of 3.22.
In Table 3 we report missing growth for Retail Trade and Restaurants
combined, where we aggregate these two industries using Tornqvist
employment shares. Due to the higher σ estimate for Retail, the Visa data
implies lower missing growth (1.26 percentage points per year) than when we
use Hall (2018) σ values (1.68), and a correspondingly smaller contribution to
aggregate missing growth of 23 vs. 30 basis points per year.
We next show the broader sensitivity of missing growth to the degree of
substitution across plants. As shown in (8), missing growth is proportional to
21
Dolfen et al. (2018) estimate 79 cents in direct costs (fuel, depreciation) and 80 cents in
indirect costs (opportunity cost of time based on after-tax wages), for a total of $3.18 per
roundtrip mile. We follow them in using cardholder and store locations to calculate driving
distance to stores, and multiplying the distance by this cost per mile. In using average spending
per visit across the two merchants for pjk , we are assuming that the price and bundle of items
bought is the same at competing merchants, other than quality differences.20
Table 3: Average missing growth for Retail Trade and Restaurants combined
Using Using
Hall σ’s Visa σ’s
Missing growth in the sector 1.68 1.26
Contribution to overall missing growth 0.30 0.23
1/(σ − 1). Thus missing growth declines monotonically as we raise σ in Table 4.
The higher is σ, the smaller the quality and variety improvements by new
plants to needed explain the observed decline in the observed market share of
continuing plants.
Table 4: M ISSING G ROWTH WITH DIFFERENT ELASTICITIES σ
Missing Growth
Higher elasticities Benchmark Lower elasticities
1983–2013 0.43 0.54 0.72
1983–1995 0.42 0.52 0.69
1996–2005 0.38 0.48 0.64
2006–2013 0.52 0.65 0.87
Note: The Benchmark columns uses σ values from Hall (2018). The Higher elasticities are 25% higher
than the σ − 1 values estimated by Hall, and the Lower elasticities are 25% lower than Hall’s.
Using payroll to measure market shares Table 5 compares missing growth
based on employment vs. payroll. The payroll data allows us to do this only
from 1989 onward. The estimates are quite similar overall, but exhibit a bigger
dip and bounce back across the three sub-periods.21
Table 5: M ISSING G ROWTH WITH E MPLOYMENT VS . PAYROLL
Employment Payroll
1989–2013 0.59 0.56
1989–1995 0.66 0.72
1996–2005 0.48 0.31
2006–2013 0.65 0.73
Note: Entries are percentage points per year.
Using revenue to measure market shares For manufacturing only, we have
access to revenue data through the Census of Manufacturing (CMF). The CMF
is available every 5 years. To calculate missing growth with lag k = 5 in a census
year t, we define incumbents as plants that are in the census in year t and t − 10
and calculate the market share growth of incumbents between year t − 5 and t.
We convert this growth over 5 years to annual growth by taking logs and dividing
by 5. We then use σ = 3.44 for manufacturing from Hall (2018) to convert the
resulting annualized growth into missing growth. Table 6 provides our missing
growth estimates based on revenue versus employment for manufacturing. The
time periods are altered slightly to coincide with Census years.
The market share of continuing manufacturing plants shrinks more in terms
of revenue than employment, so that missing growth based on equation (8) is
higher when market shares are measured in terms of revenue. As shown, there is
little missing growth in manufacturing except for the end period, so on average
this increase is relative to a small contribution. The last column of the table
displays missing growth from LBD manufacturing plants for the same periods.
The CMF and LBD yield similar missing growth for manufacturing, except for
over 2007–2012.22
Table 6: M ISSING G ROWTH WITH R EVENUE VS . E MPLOYMENT
Revenue Employment Employment
(CMF) (CMF) (LBD)
1982–2012 0.04 –0.05 –0.06
1982–1997 0.09 0.05 0.14
1997–2007 0.06 –0.25 –0.37
2007–2012 0.48 0.33 0.06
Note: All entries are for manufacturing only. For CMF, entries are averages over
quinquennial data. For LBD, entries are averages of annual data.
Different lag k Our baseline results in Table 2 evaluate the market share of
entrants after a lag of k = 5 years. Table 7 indicates how the results change if we
instead look at market shares with no lag after entry. With k = 0 missing growth
is much smaller, averaging 23 basis points per year rather than 54 basis points.
Though not reported in Table 7, for k = 3 we obtain estimates of missing growth
closer to k = 5. Increasing the lag beyond the baseline to k = 7 years increases
missing growth only slightly compared to k = 5.
Table 7: M ISSING G ROWTH WITH DIFFERENT LAGS k
k=5 k=0
1983–2013 0.54 0.23
1983–1995 0.52 0.24
1996–2005 0.48 0.27
2006–2013 0.65 0.14
Notes: Entries are percentage points per year.23
Missing growth with more sectors Our baseline estimate of missing growth
assumes a given elasticity of substitution across all plants within a 2-digit
sector. We also calculated missing growth at a more detailed level and then
aggregated the missing growth rates using Tornqvist employment shares within
each subsector as weights (again, a second order approximation to any smooth
utility aggregator). Within subsectors we set the elasticity of substitution equal
to the Hall (2018) estimate for the 2-digit sector containing the subsector.
Table 8 compares our benchmark missing growth estimates to those
obtained by aggregating up missing growth in this way up from the 3-, 4-, or
5-digit sectoral level. We present our baseline 2-digit estimates as well, for
comparison. The estimates are gently increasing in the level of disaggregation
(from 54 basis points to 65), and are broadly similar across sub-periods.22
Table 8: M ISSING GROWTH WITH DISAGGREGATED SECTORS
2-digit 3-digit 4-digit 5-digits
1983–2013 0.54 0.56 0.57 0.65
1983–1995 0.52 0.53 0.46 0.58
1996–2005 0.48 0.54 0.63 0.68
2006–2013 0.65 0.64 0.70 0.72
Notes: Entries are percentage points per year. The first column
repeats our baseline results. Other columns are Tornqvist
employment-weighted averages of missing growth within different
NAICS (2002) n-digit levels.
Declining dynamism and missing growth One may wonder why our missing
growth estimates do not trend downward along with rates of entry, exit and job
reallocation across firms — the “declining dynamism” documented by Decker
22
We also aggregated sectoral missing growth rates using average employment shares
over the entire 1983–2013 period to fully eliminate any trends due to changes in sectoral
composition. The results were very similar to those in Table 8.24
et al. (2014). The answer is three-fold. First, we look at plants (establishments)
not firms. Second, our market share equation for missing growth is tied to the
net entry rate (weighted by employment), not the gross job creation rate due
to entrants. Put differently, the growth of survivors’ market share is influenced
by the difference between the job creation rate due to new plants and the job
destruction rate due to exiting plants. Unlike gross flows at the firm level, we
see no trend in the net job creation rate of plants over 1983–2013 in the LBD.
Finally, we look at market shares five years after the plant appears in the LBD,
rather than immediately upon entry.
Table 9 illustrates these points of distinction between our market share
approach and declining dynamism. Across the first two columns, missing
growth drops dramatically when moving from plants to firms. Many new
plants are at existing firms, and they are bigger on average than new plants in
new firms.23
Table 9: M ISSING GROWTH VS . DECLINING DYNAMISM
Plant level Firm level Net entry Gross entry
1983–2013 0.54 0.15 0.29 0.29
1983–1995 0.52 0.17 0.27 0.41
1996–2005 0.48 0.16 0.32 0.29
2006–2013 0.65 0.10 0.27 0.09
Notes: Entries are percentage points per year.
The third column of Table 9, labeled “Net Entry”, shows how big missing
growth would be using firm-level data and assuming all firms were of the same
size (i.e., had the same level of employment). In this case, missing growth is
23
We identify firms using the LBD firm id, which can change with mergers and acquisition
events. We also calculated firm-level missing growth using an alternative firm id for each plant,
where we set the firm id of a plant to its initial firm id throughout the lifetime of the plant. We
find higher firm-level missing growth (0.31 percent per year versus 0.15 over 1983–2013) after
netting out M&A activity in this way.25
larger than the firm-level estimate because entering firms tend to be smaller
than the average firm.
Finally, the gross entry rate has declined more than the net entry rate, and
our missing growth estimates focus on the net entry rate. To illustrate this point,
the last column of Table 9 shows missing growth if all firms were equal-sized and
the exit rate was fixed to the 1983–2013 average. Missing growth declines even
more precipitously when measured in this counterfactual way. In the data, the
exit rate fell along with the entry rate, dampening the decline in missing growth.
To recap, declining dynamism is seen most strikingly in the gross entry rate,
which is several steps removed from our missing growth calculation. We base
our missing growth estimates on plant dynamics, rather than firm dynamics,
because we think it is much defensible to assume plants do not add new
products than to assume that firms do not do so.
4 External validation
Here we compare our sectoral missing growth estimates with those in two
prominent papers that used more detailed data on prices and quantities, and
to those obtained using a separate, indirect inference approach.
4.1 Bils (2009) and Broda and Weinstein (2010)
Bils (2009) uses scanner data to estimate quality bias in the CPI for consumer
durables. He estimates a bias of 1.8% per year from 1988–2006. To obtain a
comparable estimate, we first restrict our attention to Census retail NAICS for
durable consumer goods, which include 441 (Motor Vehicle and Parts Dealers),
442 (Furniture and Home Furnishings Stores), and 443 (Electronics and
Appliance Stores). Comparing stores of competing chains in these categories,
we estimate σ = 7.9 using Visa data. With this Visa-based σ and the market
share of continuers in the LBD in these industries, we arrive at missing growth26
of 0.36 percentage points per year from 1988–2006. This compares to 1.8
percentage points per year in Bils (2009). Bils’s number is understandably
higher because he includes understated improvements of incumbent
products, whereas our focus is solely on new outlets.
Similarly, we can restrict attention to grocery and drug store retailers to
facilitate comparison to Broda and Weinstein (2010). We map this to retailers
selling nondurables other than gasoline: categories 445 (Food and Beverage
Stores) and 446 (Health and Personal Care Stores). Comparing Visa spending at
stores within these industries, we estimate σ = 6.0. We then combine this σ with
data on continuer shares in the LBD for these industries over the period
1994–2003. We find annual missing growth of 0.43 percentage points per year,
compared to the Broda and Weinstein (2010) estimate of 0.8 percent per year.
Again, our estimate should be smaller in that we focus on new outlets, whereas
their estimate would capture improvements in products at continuing
retailers.
4.2 Indirect inference approach
Our market share approach is simple and intuitive. It does, however, require
that a plant not add new product lines — all creative destruction must occur
through new plants. Furthermore, it cannot separate out expanding variety
from creative destruction. We therefore entertained an alternative “indirect
inference” methodology which does not rely on such assumptions. This
methodology starts from the decomposition of missing growth into its creative
destruction and variety expansion components. We use the exact growth rate,
but for intuition the approximate growth decomposition is useful:
λd γdσ−1 − 1 + λn γnσ−1 − λd λi γiσ−1 − 1
M Gt ≈ .
σ−1
where λd (λn ) is the sum of the arrival ruate of creative destruction (new variety)
innovation by incumbents and entrants.27
We estimate missing growth and its decomposition by first estimating the
frequency and size of the various types of innovation, i.e., by estimating
(λi , γi , λd , γd , λn , γn ). This in turn requires more data moments than when using
the market share approach. This method is built on Garcia-Macia, Hsieh and
Klenow (2018) (hereafter GHK), who back out arrival rates and step sizes
(λi , γi , λd , γd , λn , γn ) by inferring parameter values to mimic moments on firm
dynamics in the LBD. In the Appendix we describe the GHK algorithm in some
detail. We modify it to incorporate how measured growth can differ from true
growth; GHK assumed that growth was measured perfectly.
Table A1 in the Appendix reports our indirect inference estimates — both
parameter values and the missing growth they imply. We find more missing
growth under this indirect inference approach (99 basis points per year on
average) than under the market share approach (54 basis points per year). But,
like the market share approach, the indirect inference approach yields no big
acceleration in missing growth to account for the sharp slowdown in measured
growth over 2003–2013. Finally, the indirect inference approach implies that
the vast majority (over 80%) of missing growth is due to creative destruction.
Expanding varieties play a limited role.
5 Conclusion
In this paper we lay out a model with incumbent and entrant innovation to
assess the unmeasured TFP growth resulting from creative destruction. Crucial
to this missing growth is the use of imputation by statistical agencies when
producers no longer sell a product line. Our model generates an explicit
expression for missing TFP growth as a function of the frequency and size of
creative destruction vs. other types of innovation.
Based on the model and U.S. Census data for all nonfarm businesses, we
estimated the magnitude of missing growth from creative destruction over the
period 1983–2013. Our approach uses the market share of surviving, entering,28
and exiting plants. We found that: (i) missing growth from imputation was
substantial at around half a percentage point per year — or over one-fifth of
measured productivity growth; and (ii) it has accelerated modestly since 2005,
so that it accounts for only about one-tenth of the sharp growth slowdown
since then.
We may be understating missing growth because we assumed there were no
errors in measuring quality improvements by incumbents on their own
products. We think missing growth from imputation is over and above (and
amplified by) the quality bias emphasized by the Boskin Commission.24
Our analysis could be extended in several interesting directions. One would
be to look at missing growth in countries other than the U.S. A second
extension would be to revisit optimal innovation policy. Based on Atkeson and
Burstein (2018), the optimal subsidy to R&D may be bigger if true growth is
higher than measured growth. Conversely, our estimates give a more
prominent role to creative destruction with its attendant business stealing.
A natural question is how statistical offices should alter their methodology
in light of our results, presuming our estimates are sound. The market share
approach would be hard to implement without a major expansion of BLS data
collection to include market shares for entering, surviving, and exiting
products in all sectors. The indirect inference approach is even less conducive
to high frequency analysis. A feasible compromise might be for the BLS to
impute quality growth for disappearing products based on its direct quality
adjustments for those surviving products that have been innovated upon.25
Our missing growth estimates have other implications which deserve to be
explored further. First, ideas may be getting harder to find, but not as quickly
as official statistics suggest if missing growth is sizable and relatively stable.
24
Economists at the BLS and BEA recently estimated that quality bias from health and ICT
alone was about 40 basis points per year from 2000–2015 Groshen et al. (2017).
25
Erickson and Pakes (2011) suggest that, for those categories in which data are available to
do hedonics, the BLS could improve upon the imputation method by using hedonic estimation
that corrects for both the selection bias associated with exit and time-varying unmeasured
characteristics.29
This would have ramifications for the production of ideas and future growth
(Gordon, 2012; Bloom et al., 2017). Second, the U.S. Federal Reserve might
wish to raise its inflation target to come closer to achieving quality-adjusted
price stability. Third, a higher fraction of children may enjoy a better quality of
life than their parents (Chetty et al., 2017). Fourth, as stressed by the Boskin
Commission, U.S. tax brackets and Social Security benefits may rise too steeply
since they are indexed to measured inflation, the inverse of measured growth.
A Appendix: The indirect inference method
In this section we provide an alternative, indirect inference approach to
quantify missing growth. It allows us to, in principle, separate the two sources
of missing growth — creative destruction and variety expansion. The method
relies on first estimating the arrival rates and step sizes in the model of Section
2 and then calculating missing growth based on formulas derived from the
model. To estimate the arrival rates and step sizes, we adapt the algorithm
developed in Garcia-Macia, Hsieh and Klenow (2018), henceforth GHK.
The original GHK algorithm GHK’s algorithm uses indirect inference to
estimate the step size and arrival rate of three types of innovation: Own
innovation (OI), Creative Destruction (CD), and New Varieties (NV). GHK
estimate these parameters to fit aggregate TFP growth; the mean, minimum
(one worker), and standard deviation of employment across firms; the share of
employment in young firms (firms less than 5 years old); the overall job
creation and destruction rates; the share of job creation from firms that grew
by less 1 log point (three-fold) over a five year period; employment share by
age; exit rate by size; and the growth rate in the number of firms (which is equal
to the growth rate of employment in the model).26 They calculate these
26
GHK assume each variety carries an overhead cost. Firms choose to retire a variety if the
expected profits from that variety do not cover the overhead cost. GHK calibrate the overhead
cost to match minimum employment in the data.You can also read
